1. Introduction

Realizing photonic integrated circuits on microchips has generated considerable research in the field of silicon-based waveguide-coupled planar microresonators. Interest in these types of microresonators arose due to their compact size and their ability to confine high-Q whispering-gallery modes (WGMs) by total internal reflection at the resonator sidewalls [1]. The ability to fabricate these microresonators with conventional and well developed lithographic and etch processes, makes it even more desirable. Examples of these microresonators are the microdisk and -ring resonators [2, 3]. They have been extensively investigated but suffer from a short interaction length between the straight waveguide and the curved sidewall of the resonator. This imposes a tight fabrication constraint on the waveguide width, coupling gap, and sidewall roughness. In order to increase the lateral coupling between the straight waveguide and the resonator a longer waveguide-resonator interaction length is necessary. Alternate planar resonators such as racetrack and polygonal cavities have been proposed to ease this problem [4]. The race track resonator consists of two parallel waveguides, allowing for the long interaction length with the coupling waveguide, which are connected by a 1800 curved waveguide section. However the racetrack microresonator has disadvantages: mode mismatch at the straight to curve waveguide junctions and additional fabrication roughness on the inner sidewall impose substantial cavity losses. Another alternate planar microresonator proposed is the polygonal cavity. Triangular, square, hexagonal, and octagonal waveguide-coupled microresonators have been investigated for use as add-drop filters [4-10]. The square microresonator has also been studied by our group for the purpose of a laser cavity [11]. It was during that time that the modified square microresonators [4, 12] were discovered. The modification is done to the corners of the square cavity. It has been shown that by introducing a 45o cut at the corners of the square cavity, a higher quality factor (Q-factor) for this cavity can be attained due to the suppression of standing waves in the cavity [4]. Q-factors in the order of 10⁴ have been reported for square cavities with side lengths as short as 2 µm [1].

In this paper, we present the analysis, fabrication, and characterization of the modified waveguide-coupled square microresonators. Two- and three dimensional finite difference time domain (FDTD) analysis is used to optimize the waveguide-resonator coupling and to identify the optimum corner-cut length. Fabrication of this device is done on silicon-on-insulator (SOI) by conventional e-beam lithography and dry etching techniques. The challenges in obtaining vertical and smooth resonator sidewalls are described in detail. We will also present the experimental results that are in excellent agreement with our rigorous electromagnetic analysis.

2. Design and analysis

We employ a commercially available two- and three dimensional FDTD tool by EM Photonics [13] to extensively analyze the planar waveguide-coupled square microresonator. A square microresonator, with side length L, coupled to two single mode waveguides with widths w is considered. Figure 1 shows a schematic of the analyzed structure. The coupling waveguides are labeled Input, Throughput, Drop, and Add, as depicted in the figure below. The square cavity and the coupling waveguides are separated by an air gap distance g, which has a significant effect on the coupling efficiency and Q-factor. The corners of the square cavity are cut at a 45o angle at a distance c away from the sidewalls, which is referred to as the corner-cut length. An index of refraction of n₁=1 and n₂=3.5 is used for air and silicon respectively. In the interests of time and resources, most analyses are done using two dimensional FDTD. Once a set of devices are fabricated, three dimensional FDTD is used for a better representation of the experimental results. In the two dimensional FDTD analysis, a lower index of refraction is used for silicon, n₂=3.0, to more accurately represent the fabricated device in which the mode extends in to the underlying SiO₂ layer. The underlying SiO₂ creates an asymmetry that has to be accounted for when analyzing using two dimensional FDTD. Subsequently, an excellent agreement between the analysis and experimental data will be shown.

 

Fig. 1. Schematic of waveguide-coupled corner-cut square microresonator.

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The simulation parameters consist of a Gaussian pulse centered at vacuum wavelength of 1.5 µm with a bandwidth of 10¹⁴ Hz. Virtual detectors are positioned at the throughput, drop and add ports. The structure is placed within a perfectly match layer (PML) of at least 8 grid points to absorb stray field at the simulation boundaries. In most cases we have used a 20 nm spatial resolution to keep a moderate simulation time. All simulations presented in this paper are for TE polarization, E-field in plane. Similar studies can also be performed for TM polarization as has been shown by other researchers [1, 4].

From our analysis it was concluded that coupling gap has significant dependence on the cavity properties. It has significant effects on the quality factor and drop efficiency. By increasing the coupling gap, the Q-factor increases due to the reduction of coupling losses while the drop efficiency decreases, as expected. In our case we use a coupling gap of g=200 nm and a waveguide width of w=280 nm. This coupling gap width allows for a good Qfactor while maintaining a moderate coupling efficiency. The corner-cut length also has a significant effect on the square microresonator and it will be shown that an optimal length can be found.

 

Fig. 2. (a)-(h). Three dimensional FDTD simulation of corner-cut square resonator with a resonator length L=2 µm, waveguide width w=280 nm, air gap g=200nm, height of 260 nm, and various corner-cut lengths.

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Subsequently we analyzed the effect of the corner-cut length on the properties of the cavity. The corner-cut length is varied from c=0 nm to c=350 nm for a cavity with length, coupling gap, and waveguide width of 2 µm, 200 nm, and 280 nm, respectively. The device height is 260 nm with a 1 µm silicon dioxide buffer layer underneath. The analysis was done using a fast three dimensional FDTD tool that runs on the graphics processor unit of the computer [13]. Figures 2(a) – 2(h) shows the throughput spectra of the waveguide-coupled corner-cut square microresonator with c=(a) 0 µm, (b) 50 nm, (c) 100 nm, (d) 150 nm, (e) 200 nm, (f) 250 nm, (g) 300 nm and (h) 350 nm.

By analyzing these results some interesting properties can be noted. The resonance labeled I exhibits an increase in Q-factor and drop efficiency as the corner-cut length approaches the optimum length of about 250 nm while beyond that length it starts to decrease. This enhancement is attributed to the suppression of standing waves inside the cavity as the corner-cut length approaches the optimum length. The slight shift to shorter wavelength is due to the cavity size reduction. To assure we are considering the same resonance as we change the corner-cut length, we compare the mode profile for the resonance as we vary the corner-cut length. Another interesting observation is that resonance III does not exhibit a blue shift until resonance II overlaps with it. As the corner-cut length increases beyond c=200 nm, the combined resonance fades away since it is no longer a supported mode of the cavity. The steady state mode profile for the combined resonance of II and III has no resemblance to the individual resonances prior to their overlap. Once the corner-cut length goes beyond c= 350 nm for a cavity length of 2µm it starts to behave as an octagonal microresonator [12]. Figure 3 show the mode profile for resonances I and II+III.

 

Fig. 3. Magnetic field for resonance (a) I and (b) II+III, calculated using FDTD technique.

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3. Fabrication and characterization

One advantage of this microresonator is that it can be fabricated with conventional e-beam lithography and dry etching techniques. The performance of the microresonator can significantly be hindered by rough sidewalls and tapered sidewall angles [15]. Both the lithographic and etch processes have been optimized to achieve vertical and smooth sidewalls. The device is patterned on SOI with a device layer of 260 nm. Coupling light in and out of the 250 nm single mode waveguides is challenging. A simple approach is to use adiabatic linear tapers to go from a 5 µm to 250 nm waveguide. These adiabatic linear tapers require a large foot print and are highly sensitive to both the taper length and sidewall roughness which makes them undesirable. In our case a taper length of at least 200 µm was necessary for a moderate coupling to the single mode waveguide. An alternate approach is to use an in-plane parabolic mirror, the J-Coupler [14], shown in Fig. 4(a). The J-Coupler reduces the foot print, making it easier to fabricate, and is less sensitive to sidewall roughness. With this design we were able to fabricate J-couples than can couple light to waveguides as small as 100 nm with minimal effort.

 

Fig. 4. SEM micrograph of (a) J-Coupler and (b) square microresonator with a 100 nm corner-cut length. The inset in (a) is a zoomed out image of the device.

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The first step in the fabrication process is to pattern the device on SOI using an e-beam lithography tool. A low beam current and speed is used for better control of the small features and to reduce sidewall roughness. This step is followed by an anneal at 120°C, just below the melting temperature of PMMA, to smooth out the sidewalls of both the microresonator and coupling waveguides. The resulting pattern is then transferred in to the silicon layer by a dry etch process. The dry etch process is a highly anisotropic Fluorine based Bosch etch performed on an Inductively Coupled Plasma etch system. The cyclic etch and passivation steps in the Bosch process are carefully balanced and optimized to reduce the rippling effects commonly seen in this type of etch. The resulting devices show near vertical and smooth sidewalls, see Fig. 4(b), which is necessary for good performance. The final process step is an oxygen ash to remove the residual e-beam resist. To prep the sample for characterization, it is cleaved or diced though the large waveguides to allow coupling from a fiber to the microresonators.

Characterization of these devices was performed using a tunable Agilent laser source. The laser source was fiber coupled in to the input port and detected at both the through- and drop ports. For both the input coupling and output collection a tapered lensed fiber was used. As can be seen from Fig. 5, the measured results are in excellent agreements with the simulations. These particular devices have a cavity length of L=2µm, waveguide width of w=280 nm, coupling gap of g=180 nm, and various corner-cut lengths. The smaller coupling gap after fabrication was a result of the tight tolerances of the entire fabrication process. Additional simulations were conducted with a coupling gap of g=180 nm to more accurately reflect the performance of this particular device. The simulation shows that an optimum performance can be achieved for the 1305 nm resonance with a corner-cut length of roughly 200 nm. This agrees well with the experimental data. It can be noted that the no-corner-cut and 100 nm corner-cut devices have almost identical performance. This is due to the difficulty in fabricating a perfect corner for the cavity at these small dimensions. SEM micrograph shows that the no-corner-cut device has some rounding at the edges which has a close resemblance to the 100 nm corner-cut device. A small second peak can be noted for c=200 nm in the experimental measurement and not in the simulated data. This is due to the geometric disparity between the simulated and experimental device due to imperfection in the fabrication process. A Q-factor greater than 420 has been measured for the cavity with the optimum corner-cut length. This is a about a factor of two enhancement compared to the no-corner-cut cavity. We characterized multiple resonances on this set of devices and similar performance and behavior was observed. Extremely low throughput limited the measurement of resonances at longer wavelengths due to the cut-off wavelength for TE polarization in the coupling waveguide. The inset in Fig. 5(b) shows the mode profile for this resonance.

 

Fig. 5. Spectrum of the drop port showing a resonance at about 1305 nm for various cornercut lengths, (a) experimental and (b) simulation. Excellent agreement between simulations and experimental data can be noted. Inset in (b) shows the mode profile for this resonance.

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4. Conclusion

In summary, we presented the design, fabrication, and characterization of a waveguide-coupled square microresonator with altered corners. Our rigorous electromagnetic analysis shows significant improvement for a square cavity with an optimum corner cut versus a no-corner-cut cavity. Interesting cavity phenomena associated with varying corner-cuts were presented and analyzed. Following the design, fabrication of these waveguide-coupled square cavities is discussed in detail. Characterization of these cavities shows an excellent agreement with the simulations. A measured Q-factor of about 420 is shown which is about a 2x enhancement over a cavity with no-corner-cut for this particular resonance. A further improvement of the Q-factor can be achieved if the square cavity is combined with precisely engineered dispersion based photonic crystals. We strongly believe that carefully designed square microresonators with optimum corner-cut alteration, are a promising building block for high-index contrast integrated photonic circuits.